Colorado School of mines have a comprehensive lecture in solid state physics. And describes this derivation of the effective mass using Newton's second law. http://solidstate.mines.edu/videonotes/VN_10_2.pdfM Quack said:
Effective mass is a measure of the inertia of a particle in a solid or a crystal lattice. It is a concept used in condensed matter physics to describe the behavior of electrons or other particles in a material. It is defined as the mass of an electron in free space multiplied by a factor that takes into account the effects of the crystal lattice on the electron's motion.
Effective mass is calculated using the band structure of a material, which is a graph that shows the allowed energy levels for electrons in a crystal lattice. The effective mass is determined by taking the curvature of the band structure at a specific energy level and comparing it to the curvature of the free electron band. The ratio of the two curvatures gives the effective mass.
Effective mass is a useful concept in understanding the behavior of electrons and other particles in a material. It is used in various applications such as semiconductor devices, where the effective mass of electrons determines the conductivity of the material. It is also used in the study of optical and electronic properties of materials, as well as in the development of new materials for specific purposes.
The effective mass of electrons plays a crucial role in determining their mobility, which is the ability to move freely in a material. A lower effective mass means that the electrons can move more easily, resulting in a higher mobility. This is why materials with a lower effective mass, such as metals, have higher electrical conductivity compared to materials with a higher effective mass, like insulators.
The effective mass of a material is temperature dependent. As the temperature increases, the crystal lattice of the material vibrates more, causing the effective mass to increase. This is because the increased vibrations make it more difficult for the electrons to move through the lattice, resulting in a higher effective mass. Therefore, the effective mass of a material is not a constant value and can change with temperature.
